Q.42

Expert-verified
Found in: Page 332

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# What are the magnitude and direction of the angular momentum relative to the origin of the particle

Hence the momentum of the particle is

See the step by step solution

## Step :1 Introduction

In the same manner that torque is the rotational equivalent of force, angular momentum is the rotational equivalent of linear momentum. In vector notation, angular momentum is given by

Here is the position vector of the particle and is the momentum vector of the given particle.

## Step : 2 Explanation

The travelling particle's direction is depicted in the diagram below.

## Step :3 Moving in direction

The particle is travelling with a velocity of in a direction below the positive -axis. The particle's horizontal and vertical components of velocity are then calculated.

And

## Step : 4 Mass of the particle

The mass of the particle is

The given particle lies in the plane. Then position vector of the given particle is

And velocity vector of the given particle is

## Step :5 Angular momentum

Since angular momentum is the rotational equivalent of linear momentum in much the same way that torque is the rotational equivalent of force. Angular momentum in vector notation is given by